Up to the 'sixties, Roman Catholic priests were required to celebrate
Mass in a standing position, even those with disabilities. What was
the theological reason behind this and why and when was it changed?

According to articles found in A Dictionary of Liturgy and Worship, in
the Primitive Church everyone except the presiding bishop or
presbyter, and the elderly for whom seats were provided, stood during
the mass. The Gregorian sacramentary of the seventh century became
standard. The ceremonial directions for the mass, based on the Ordo
Romanus Primus, the ceremonial for the papal mass, became increasingly
complex through the Middle Ages, and the Ordinale, a special book of
directions was compiled. The mass evolved and diversified to
accommodate the inclusion of the non-Latin nations, and clerical
ceremonial aspects were stressed over the communal, with the papal
mass dominating and eventually being fixed universally for the Roman
Church as defined by the Tridentine Mass in the missal issued by Pius
V in 1570. Gradually, the directions of the Ordinale were incorporated
into the missal as Rubrics, so-called because they were printed in
red, which included rubrics regarding postures of the clergy and laity
during the mass. The reforms of the missal following the Second
Vatican Council of 1962 resulted in the restoration of flexibility in
the mass and the participation of the laity, as reflected in the new
missal of 1969.

See articles on Liturgies, Mass (High), Mass (Low), Postures, Roman
Catholic Worship, and Rubrics in:

A Dictionary of Liturgy and Worship, ed. Davies, J.G., Macmillan, New
York, 1972.

hlabadie-ga

As a long-time Catholic I can tell you that many things done in the Church
are done out of tradition, not because of theological reasons. Perhaps
the standing was done simply out of practicality, so more people could
see. And the change may have been simply due to heightened sensitivity 
to the disabled. The Second Vatican Council may have addressed the issue,
or the change may have simply come about spontaneously. cath-ga

Because of tradition that evolved out of conventional, perhaps
genetically determined body language.  In the presence of a monarch,
or authority, sitting would indicate two equal powers.  One would bow
in the presence of a greater authority, or kneel to show subserviance
to the greater power.  This action might be genetically programmed as
a signal of subserviance.  For instance, in the animal kingdom, where
a pecking order is acknowledge, a dog, or another animal will lower
its head to show submission.  Similarly, a priest could not, through
body language, sit while communing with God, because it would indicate
a lack of recognition of a greater power.  Kneeling, or genuflecting,
occurs in the Mass as an acknowledgement of the presence of God, and
as an acknowledgement of the presence of a greater power. 
Traditionally, when a person kneels or bows in the presence of an
authority other than God, this is not done from a sitting position,
since that would imply an equality of power.  Someone might be invited
to sit, after kneeling before a greater power, but rarely because that
would obfusicate the power roles.